Year: 2026
Type: preprint
Abstract: We present exact analytical solutions to the nonlinear relativistic Boltzmann equation for homogeneous, isotropic massless multi-component systems with non-isotropic scattering cross sections. For a two-component system, we identify three distinct classes of exact solutions, each corresponding to specific constraints among initial energy densities, particle number densities, and scattering cross sections. These solutions comprise the equilibrium state and two novel classes: a hybrid structure featuring a non-equilibrium Maxwell-Juttner distribution coupled with a nontrivial distribution; the former is unprecedented in kinetic theory, while the latter refers to nontrivial dynamics shared by both species, which is novel in the relativistic context.
Source: arXiv (Cornell University)
Authors: Wei, Linyuan, Wang, Yi, Hu, Jin, Chen, Baoyi
Institutions: Tianjin University, Tsinghua University, Fuzhou University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2013753141
OpenAlex ID: W7214210886